BAEssd (version 1.0.1)

binom1.1sided: Binomial Suite: One Sample, One Sided

Description

Generates the suite of functions related to the one sample binomial experiment with a one-sided alternative hypothesis of interest.

Usage

binom1.1sided(p0, a, b)

Arguments

p0

Scalar. The upper bound of p under null hypothesis Ho: p

a

Scalar. Shape1 parameter for prior Beta distribution. See documentation for dbeta.

b

Scalar. Shape2 parameter for prior Beta distribution. See documentation for dbeta.

Value

binom1.1sided returns a list of 4 functions. These functions are useful for either visualizing the problem, or computing the required sample size:

logm

The function returns a list of three vectors: the log marginal density under the null hypothesis (logm0), the log marginal density under the alternative hypothesis (logm1), and the log marginal density (logm). Each are evaluated at the observed data provided. This function is also passed to ssd.binom to calculate required sample sizes. This function has the following usage:

logm(x, n, p0, a, b)

• x: Vector. Number of successes observed, out of n independent Bernoulli trials.
• n: Scalar. Sample size, the number of independent Bernoulli trials.
• Remaining parameters are specified above for binom1.1sided.

logbf

Returns a vector: the value of the log Bayes Factor given the observed data provided and the prior parameters specified. This function has the following usage:

logbf(x, n, p0, a, b)

For details on the parameters for this function, see the above description for logm.

prior

Returns a vector: the value of the prior density at the specified value of p with parameters a and b. This function has the following usage:

prior(p, a, b)

• p: Vector. Quantiles at which to evaluate the prior distribution.
• Remaining parameters are specified above for binom1.1sided.

post

Returns a vector: the value of the posterior density. This function has the following usage:

post(p, x, n, a, b)

• p: Vector. Quantiles at which to evaluate the posterior distribution.
• x: Scalar. Number of successes observed, out of n independent Bernoulli trials.
• n: Scalar: The number of independent Bernoulli trials.
• Remaining parameters are specified above for binom1.1sided.

Details

binom1.1sided is used to generate a suite of functions for a one-sample binomial experiment with a one-sided alternative hypothesis. That is, when $$X \sim Binomial(n,p)$$ $$H_0: p \leq p_0 \quad vs. \quad H_1: p > p_0$$ using the following prior on p $$p \sim Beta(a,b)$$ The functions that are generated are useful in examining the prior and posterior densities of the parameter p, as well as constructing the Bayes Factor and determining the sample size via an average error based approach. The arguments of binom1.1sided are passed to each of the additional functions upon their creation as default values. That is, if p0 is set to 0.5 in the call to binom1.1sided, each of the functions returned will have the defaualt value of 0.5 for p0. If an argument is not specified in the call to binom1.1sided, then it remains a required parameter in all functions created.

See Also

binom1.2sided,binom2.1sided, binom2.2sided,norm1KV.1sided, norm1KV.2sided,norm2KV.2sided norm1UV.2sided,ssd,BAEssd

Examples

############################################################
# Generate the suite of functions for a one-sample binomial
# with a one-sided test. Consider the hypothesis
#      H0: p<=0.5   vs.  H1: p>0.5
#
# with a uniform prior on p.

# generate suite
f1 <- binom1.1sided(p0=0.5,a=1,b=1)

# attach suite
attach(f1)

# plot prior and posterior given x = 25, n = 30
ps <- seq(0.01,0.99,0.01)
p1 <- prior(ps)
p2 <- post(ps,x=25,n=30)

plot(c(p1,p2)~rep(ps,2),type="n",ylab="Density",xlab="p",main="")
lines(p1~ps,lty=1,lwd=2)
lines(p2~ps,lty=2,lwd=2)

# perform sample size calculation with TE bound of 0.25 and weight 0.5
ssd.binom(alpha=0.25,w=0.5,logm=logm)

# detain suite
detach(f1)